To　solve　the　conflict　of　certification　and　privacy　such　as　the　electronic　election,　online　bidding　and　other　such　network　applications,　a　quantum　signature　scheme　with　public　verifiability　is　converted　into　a　designated　verifier　signature　by　introducing　the　classic　ideas　of　Diffie-Hellman　(DH)　key　exchange,　in　which　the　signer　first　generates　a　public　verifiability　initial　signature　with　the　help　of　a　trusted　third　party　according　the　quantum　signature　scheme,　and　then　the　signer　and　verifier　agree　a　secret　key,　finally　generates　the　value　of　signature　through　the　secret　key　shared　between　the　signer　and　verifier　and　the　initial　signature.　This　designated　verifier　signature　scheme　can　make　that　only　a　verifier　designated　by　a　signer　can　verify　the　＂validity　of　a　signature＂　and　the　designated　verifier　cannot　prove　to　a　third　party　that　the　signature　was　produced　by　the　signer　or　by　himself　through　a　transcript　simulation　algorithm.　The　final　research　results　will　not　only　provide　a　new　way　for　the　research　methods　of　quantum　designated　verifier　signature,　but　also　provide　a　useful　supplement　for　identity　privacy　protection　methods.　(C)　2018　Elsevier　GmbH.　All　rights　reserved.